On Matrices that are not Similar to a Toeplitz Matrix and a Family of Polynomials Tewodros Amdeberhan and Georg Heinig

Amdeberhan, Tewodros; Heinig, Georg

doi:10.1007/978-3-7643-8996-3_4

Tewodros Amdeberhan³¹ &
Georg Heinig³¹

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 199))

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Abstract

A conjecture from the second author’s paper [Linear Algebra Appl., 332–334 (2001) 519–531] concerning a family of polynomials is proved and strengthened. A consequence of this is that for any n ≥ 4 there is an n × n matrix that is not similar to a Toeplitz matrix, which was proved before for odd n and n = 6, 8, 10.

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References

Philippe Delsarte, Yves V. Genin. Spectral properties of finite Toeplitz matrices. in Mathematical Theory of networks and Systems: Proc. MTNS-83 Int. Symp., Beer Sheva, Israel, June 1983, P.A. Fhrmann, ed., Lecture Notes in Control and Information Sciences, New York, Springer-Verlag, 58:194–213, 1984.
Google Scholar
Georg Heinig. Not every matrix is similar to a Toeplitz matrix. Linear Algebra Appl., 332–334:519–531, 2001.
Article MathSciNet Google Scholar
Henry J Landau. The inverse eigenvalue problem for real symmetric Toeplitz matrices. J. Amer. Math. Soc., 7:749–767, 1994.
MATH MathSciNet Google Scholar
D. Steven Mackey, Niloufer Mackey, and Srdjan Petrovic. Is every matrix similar to a Toeplitz matrix? Linear Algebra Appl. 297:87–105, 1999.
Article MATH MathSciNet Google Scholar
Marko Petkovsek, Herbert Wilf, Doron Zeilberger. A = B Toeplitz matrices. A.K. Peters Ltd., USA, 1996.
Google Scholar
Harald K. Wimmer. Similarity of block companion and block Toeplitz matrices. Linear Algebra Appl. 343–344:381–387, 2002.
Article MathSciNet Google Scholar

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Authors and Affiliations

Mathematics, Tulane University, New Orleans, LA, 70118, USA
Tewodros Amdeberhan & Georg Heinig

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Tewodros Amdeberhan
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Georg Heinig
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Editors and Affiliations

Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo, 5, 56127, Pisa, Italy
Dario Andrea Bini
Institut für Mathematik, Technische Universität Berlin, Straβe des 17. Juni 136, 10623, Berlin, Germany
Volker Mehrmann
Department of Mathematics, University of Connecticut, 196 Auditorium Road, U-9, Storrs, CT, 06269, USA
Vadim Olshevsky
Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina Street, 8, Moscow, 119991, Russia
Eugene E. Tyrtyshnikov
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3001, Leuven (Heverlee), Belgium
Marc van Barel

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Amdeberhan, T., Heinig, G. (2010). On Matrices that are not Similar to a Toeplitz Matrix and a Family of Polynomials Tewodros Amdeberhan and Georg Heinig. In: Bini, D.A., Mehrmann, V., Olshevsky, V., Tyrtyshnikov, E.E., van Barel, M. (eds) Numerical Methods for Structured Matrices and Applications. Operator Theory: Advances and Applications, vol 199. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8996-3_4

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DOI: https://doi.org/10.1007/978-3-7643-8996-3_4
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8995-6
Online ISBN: 978-3-7643-8996-3
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